Prospects of different lotteries
In the following we discuss the prospects of three german lotteries: “6 aus 49”, “Keno” and “Eurojackpot”. The last one is in several european countries available.
6 aus 49
The aim of “6 aus 49” is to match 6 random numbers in an interval from 1 to 49 plus a so called super number, which is the last digit of the game ticket number.
The probabilities are displayed in the table below (derived from wikipedia).
The chance of a win in the highest class is only 1:139.838.160 while the chance of earth being hit by a doomsday asteroid with a diameter of 3300 ft within a year is 1:440.000. So after 318 doomsday asteroid hits you may have a win in the highest class of “6 aus 49”? Well, if you play every week “6 aus 49” you need only 6 asteroids 😉
| class | combinations | possibilities | in % (rounded) |
|---|---|---|---|
| I | 6 hits + super number | 1 / 139.838.160 | 0,000000715 % |
| II | 6 hits – super number | 9 / 139.838.160 ≈ 1 / 15.537.573 | 0,00000644 % |
| III | 5 hits + super number | 6 / 13.983.816 = 1 / 2.330.636 | 0,0000429 % |
| IV | 5 hits – super number | 252 / 13.983.816 ≈ 1 / 55.491 | 0,00180 % |
| V | 4 hits + super number | 630 / 13.983.816 ≈ 1 / 22.197 | 0,00451 % |
| VI | 4 hits – super number | 12.915 / 13.983.816 ≈ 1 / 1.083 | 0,0924 % |
| VII | 3 hits + super number | 17.220 / 13.983.816 ≈ 1 / 812 | 0,123 % |
| VIII | 3 hits – super number | 229.600 / 13.983.816 ≈ 1 / 61 | 1,64 % |
probabilities of “6 aus 49” (derived from Wikipedia)
Keno
Let’s have a look to “Keno”.
The player have to select 2 to 10 numbers out of an interval from 1 to 70. The lottery will draw 20 random numbers.
You can see the probabilities for the different combinations in the table below.
The chance of a win in the highest class is here 1:2.147.179 compared to 1:139.838.160 in “6 aus 49”.
And if you play “Keno” every week, you need no doomsday asteroid for a win in the highest class.
This is the good news.
| selected numbers | hits | possible combinations | possibility | factor |
|---|---|---|---|---|
| 2 | 0 | 1.225 | 50,72464 % | 0 |
| 2 | 1 | 1.000 | 41,40787 % | 0 |
| 2 | 2 | 190 | 7,86749 % | 6 |
| 3 | 0 | 19.600 | 35,80563 % | 0 |
| 3 | 1 | 24.500 | 44,75703 % | 0 |
| 3 | 2 | 9.500 | 17,35477 % | 1 |
| 3 | 3 | 1.140 | 2,08257 % | 16 |
| 4 | 0 | 230.300 | 25,11738 % | 0 |
| 4 | 1 | 392.000 | 42,75299 % | 0 |
| 4 | 2 | 232.750 | 25,38459 % | 1 |
| 4 | 3 | 57.000 | 6,21663 % | 2 |
| 4 | 4 | 4.845 | 0,52841 % | 22 |
| 5 | 0 | 2.118.760 | 17,50605 % | 0 |
| 5 | 1 | 4.606.000 | 38,05664 % | 0 |
| 5 | 2 | 3.724.000 | 30,76920 % | 0 |
| 5 | 3 | 1.396.500 | 11,53845 % | 2 |
| 5 | 4 | 242.250 | 2,00157 % | 7 |
| 5 | 5 | 15.504 | 0,12810 % | 100 |
| 6 | 0 | 15.890.700 | 12,11957 % | 0 |
| 6 | 1 | 42.375.200 | 32,31887 % | 0 |
| 6 | 2 | 43.757.000 | 33,37274 % | 0 |
| 6 | 3 | 22.344.000 | 17,04140 % | 1 |
| 6 | 4 | 5.935.125 | 4,52662 % | 2 |
| 6 | 5 | 775.200 | 0,59123 % | 15 |
| 6 | 6 | 38.760 | 0,02956 % | 500 |
| 7 | 0 | 99.884.400 | 8,33221 % | 0 |
| 7 | 1 | 317.814.000 | 26,51157 % | 0 |
| 7 | 2 | 402.564.400 | 33,58132 % | 0 |
| 7 | 3 | 262.542.000 | 21,90086 % | 0 |
| 7 | 4 | 94.962.000 | 7,92159 % | 1 |
| 7 | 5 | 18.992.400 | 1,58432 % | 12 |
| 7 | 6 | 1.938.000 | 0,16167 % | 100 |
| 7 | 7 | 77.520 | 0,00646 % | 1.000 |
| 8 | 0 | 536.878.650 | 5,68706 % | 1 |
| 8 | 1 | 1.997.688.000 | 21,16116 % | 0 |
| 8 | 2 | 3.019.233.000 | 31,98221 % | 0 |
| 8 | 3 | 2.415.386.400 | 25,58577 % | 0 |
| 8 | 4 | 1.115.803.500 | 11,81951 % | 1 |
| 8 | 5 | 303.878.400 | 3,21893 % | 2 |
| 8 | 6 | 47.481.000 | 0,50296 % | 15 |
| 8 | 7 | 3.876.000 | 0,04106 % | 100 |
| 8 | 8 | 125.970 | 0,00133 % | 10.000 |
| 9 | 0 | 2.505.433.700 | 3,85253 % | 2 |
| 9 | 1 | 10.737.573.000 | 16,51083 % | 0 |
| 9 | 2 | 18.978.036.000 | 29,18193 % | 0 |
| 9 | 3 | 18.115.398.000 | 27,85547 % | 0 |
| 9 | 4 | 10.265.392.200 | 15,78477 % | 0 |
| 9 | 5 | 3.570.571.200 | 5,49035 % | 2 |
| 9 | 6 | 759.696.000 | 1,16816 % | 5 |
| 9 | 7 | 94.962.000 | 0,14602 % | 20 |
| 9 | 8 | 6.298.500 | 0,00969 % | 1.000 |
| 9 | 9 | 167.960 | 0,00026 % | 50.000 |
| 10 | 0 | 10.272.278.170 | 2,58940 % | 2 |
| 10 | 1 | 50.108.674.000 | 12,63123 % | 0 |
| 10 | 2 | 102.006.943.500 | 25,71358 % | 0 |
| 10 | 3 | 113.868.216.000 | 28,70353 % | 0 |
| 10 | 4 | 76.990.441.500 | 19,40750 % | 0 |
| 10 | 5 | 32.849.255.040 | 8,28053 % | 2 |
| 10 | 6 | 8.926.428.000 | 2,25015 % | 5 |
| 10 | 7 | 1.519.392.000 | 0,38300 % | 15 |
| 10 | 8 | 154.313.250 | 0,03890 % | 100 |
| 10 | 9 | 8.398.000 | 0,00212 % | 1.000 |
| 10 | 10 | 184.756 | 0,00005 % | 100.000 |
probabilities of “Keno” (derived from Wikipedia)
Eurojackpot
This lottery is available in Croatia, Czech Republic, Denmark, Estonia, Finland, Germany, Hungary, Iceland, Italy, Latvia, Lithuania, Netherlands, Norway, Poland, Slovakia, Slovenia, Spain and Sweden.
The aim of “Eurojackpot”” is to match 5 random numbers of an interval from 1 to 50 and 2 random numbers, the so called Euro numbers, of an interval from 1 to 10.
The prospects are displayed in the table below.
The chance to win the Jackpot (the highest class) is 1 : 95.344.200.
This is a better prospect for the highest class as in “6 aus 49” but worse than in “Keno”.
| prize category | hits in A + B | chance of winning | in % (rounded) |
|---|---|---|---|
| 1 (Jackpot) | 5 + 2 | 1 : 95 344 200 | 0,00000105 % |
| 2 | 5 + 1 | 1 : 5 959 013 | 0,00001678 % |
| 3 | 5 | 1 : 3 405 150 | 0,00002937 % |
| 4 | 4 + 2 | 1 : 423 752 | 0,00023599 % |
| 5 | 4 + 1 | 1 : 26 485 | 0,00377579 % |
| 6 | 4 | 1 : 15 134 | 0,00660764 % |
| 7 | 3 + 2 | 1 : 9 631 | 0,01038343 % |
| 8 | 2 + 2 | 1 : 672 | 0,14882919 % |
| 9 | 3 + 1 | 1 : 602 | 0,16613491 % |
| 10 | 3 | 1 : 344 | 0,29073609 % |
| 11 | 1 + 2 | 1 : 128 | 0,78135324 % |
| 12 | 2 + 1 | 1 : 42 | 2,38126703 % |
| blank | less than 3 hits | 96,21062949 % |
probabilities of “Eurojackpot” (derived from Wikipedia)
So, what is the best strategy?
… to be continued.